Calculating device



Nov. 28, 1933. J. F. sUMMERs CALCULATING DEVICE Filed April 1e, 1952Lfundwll- 11H21 .f QN W J w we/N Nw wwqwu WN Patented Nov. 28, 1933UNITED SE llfi This invention relates to calculating devices of aportable type by means ofv which various mathematical calculations canbe made.

The objects oi this invention are to provide a calculating device bymeans of which greater accuracy can be obtained by means of acalculating device occupying materially less space than isrequired forslide rules and other calculating devices of corresponding accuracy;also to provide a device of this kind which can be easily manipulated tomake calculations which when not in use can be conned in a small case;also to provide a calculating device in which the graduations by meansof which calculations are made are formed on a. flexible tape which,when not in use, may be arranged in a coil; also to improve calculatingdevices of this kind in the other respects hereinafter specified.

This invention is based on the fact that the sum of any two numbers isequal to twice their average and, consequently, if two sets ofgraduations are arranged side by side and coextensive, one set ofgraduations being of half of the scale of the other, then the average oftwo numbers on the first set of graduations will be found at a pointmidway between these numbers, and twice this average can be found on theother set of graduations at a point directly opposite the average. Thisprinciple may be carried out in higher mathematics by using other ratiosbetween the two sets of vgraduations than the 2:1 ratio above referredto.

In the accompanying drawing:

Fig. 1 is a side elevation, partly in section, of a calculating deviceembodying this invention.

- Fig. 2 is a fragmentary face view of a portion of the tape;

Fig. 3 is a perspective view of another portion of the tape;

Fig. 4 is a fragmentary perspective view of two portions oftape with aslide member arranged on one of the portions;

Fig. 5 is a side elevation of the calculating device when not in use;

Fig. 6 is a sectional View of line 6 6, Fig. 2;

Fig. Z is a sectional'view on line 7 7, Fig. 5.

The invention is shown in the accompanying drawing as applied to ailexible tape which cooperates with means for finding a midway pointbetween two other pointson the tape, but it will be understood that itis not intended to limit the invention to the particular device shown,since obviously the invention may be carried out by other means thanthose illustrated.

A represents a strip or exible tape which may,

for example, be made of steel or other material, and which when not inuse may be wound by means of a coil spring 10 upon a drum or spool 11,the spool and spring being arranged within a case 12.` All of theseparts may be or any suitable construction, such for example asheretofore used in connection with measuring tapes.

The tape is provided with a plurality of sets 0 1 graduations which, forsake of convenience 65 may be arranged at the opposite edges of thetape, and these sets of graduations are coextensive lengthwise oi thetape. One of these sets of graduations is two or more times the scale ofthe other set and the smaller set of graduations may therefore berepeated so that two or more successive sets of graduations are arrangedopposite to the larger scale set of graduations.

Referring rst to the lower portion of Fig. 3, which shows in itssimplest form the principle upon which my invention is based, the edgeportion 15 of the lower portion of the scale shown in this gure isprovided with a set of graduations spaced equally from each other andprovided with numbers arithmetically arranged. Subdivisions of thegraduations are preferably also provided, such subdivisions being onlypartly shown in Figs. 2 and 3 for the sake of clearness. On the otheredge portion 16 of the same part of the tape is arranged another set ofgraduations, the graduations in this case being half the scale o theother graduations, or in other words, the graduations on the edge 16 aretwice the number of the graduations on the edge portion 15 and arespaced half as far apart. This portion of the tape is intended to beused for addition and subtraction, and it will be noted that the numberson the graduations of the edge portion 16 are double those oncorresponding graduations on the edge portion 15, so that if any numberon the edge portion 15 is added to itself, or doubled, the answer can beread on the directly opposite side of the tape, to wit, on the edgeportion 16. If two numbers are to be added, these numbers are located onthe edge portion 15 of the tape and a point midway between these twonumbers is then found on the edge portion 16 so that by means of thegraduations on this edge of the tape the answer can be read ofi. Forexample, if the tape is` made of material that is suiiciently flexibleto permit creasing of the same, any two numbers on the scale at the edgeportion 15 can be added by doubling the tape upon itself to place thesetwo numbers directly opposite each other and then bisecting the portionof the tape between these two numbers in the usual way by creasing thetape. At the crease and on the edge portion 16 will be found the answer.For example, if 3 and 9 are to be added, the tape is flexed so that thegraduations 3 and 9 on the edge portion 15 of the tape are inregistration, and by finding the half-way position between these twonumbers on the opposite edge portion of the tape, the answer 12 can beread. Subtraction is, of course done in a similar manner. If 3 is' to besubtracted from 12, the fiexible tape could be creased at 12, so thatthe portions of the tape toward opposite ends from the crease will liein contact. In registration with 3 will be 9. When the tape is made ofmetal or other less flexible material, suitable means for finding thehalf-way position may be employed instead of creasing the tape. In orderto facilitate the use of the tape, identical graduations are preferablyformed on both faces of the tape so that, for example, the samegraduations will be formed on both faces of the edge portions of thetape.

In order to effect multiplication and division, the same principle canbe lemployed on a different tape or on a different portion of the sametape, if the opposite edge portions of the tape are provided withlogarithmic graduations. In this case again, thel graduations on theedge portion 17 of the tape are on a larger scale than the graduationson the edge portion 18, being twice the scale for ordinarymultiplication and division, although different ratios may be used forother mathematical calculations. The smaller scale graduations arerepeated so that when the scale of one set of graduations is twice thatof the other, two complete sets of graduations will be placed opposite asingle set of graduations, or if desired, the numbers on the smallerscale graduations may run from 1 to 100 while those on the larger scalegraduations run from l to 10. The logarithmic graduations may be formedin the same manner as is customary on slide rules, the numbers oppositethe graduations being natural numbers. Consequently, in order tomultiply two numbers, it is necessary to find these two numbers on thegraduations on the edge portion 17 of the tape and then 11nd a pointhalf way between these two numbers. This may be done by bending the tapeso that these two numbers are in registration. The product is found onthe opposite scale at a point halfway between these two numbers. Byreversing this procedure, division may, of course, be done. Numbers maybe squared or square roots taken by reading directly across the tapefrom one scale to the other.

Still another tape may be graduated in such a way that logarithmicgraduations are on one edge portion while the logarithms of logarithmsare used as a basis of graduation of the opposite edge portion of thescale, and by a similar manipulation of the tape, as already described,other calculations can be made which will be obvious to those skilled inmathamatics, such as raising numbers to different powers, and findingroots.

Since the tape may be of thin material. it may also be made long enoughto have different sets of graduations for adding, multiplying andraising of numbers to different powers, on different portions of thelength of the tape, or if desired, the entire length of the scale may beused for only one of these operations, in which case the accuracy of thedevice is correspondingly increased.

Any suitable means may be provided on the tape for facilitating the useof the same. For example, for placing two graduations on the tape intoregistration, a slide member 20 may be provided on the tape, this slide,as shown, being in the form of a block of metal or other material havinga slot 21 extending through the same through which the tape A may slide.The front face of the block at one side of the slide may be recessed orcut out as indicated at 22 in Figs. 2 and 4, to facilitate reading thegraduations on the tape, and the rear face of the block may be providedwith a step or ledge 24a on which the edge of another portion of thetape A may be placed, as indicated in Fig. 6. In this way, twograduations on the edge portion 17 of the tape may be placed intoregistration, as indicated in Fig. 2. During the time that the answer isbeing read, the two portions of the tape adjacent to the slide 20 can beheld in correct relation to each other by two fingers of one hand. Anyother device may be used for this purpose, or, if desired, which devicemay be entirely omitted, since two graduations can be placed intoregistration without the aid of any slide or similar device.

The device shown in the drawing for use in finding the answer may be ofany suitable or desired form for the purpose of determining the half-wayposition on the tape between the two parts in registration on theslide20. In the particular construction shown for this purpose acylinder or partly cylindrical member 25 is provided which may either berotatably or rigidly secured by means of a pin 24 to two side plates 26and 27. The cylinder 25 is preferably of such radius that the tape A canbe bent around the same without creasing or otherwise damaging the tape.These side plates may be held in correct relation to each other and tothe cylinder 25 by any suitable means such, for example, by riveting orupsetting the ends of the pin 24 against the outer faces of the sideplates, and if desired, also by a pair of posts or spacing members 28.Preferably these posts are rigidly secured to one of the plates andextend slidably through apertures in the other plate, so that the outerends of the plates connected by the posts may be moved toward and fromeach other. These posls serve to confine the tape between the cylinder25 and the posts so that the finder is permanently but movably arrangedon the tape. The plate 26 is provided in the middle portion thereof withan arrow 30 or other indicator pointing toward the edges 18 or 16 of thetape, this arrow or indicator being locatedin the longitudinal centralline of the finder. Consequently, when the two graduations on the edgeportion 17 or 15 of the tape are placed into registration and the finderis pulled away from this point of registration to bisect the portion ofthe tape lying between these two points, as shown in Fig. 1, the arrow30 will point to the correct answer on the edge portion 18 of the tape.In order to facilitate reading of the answer, the outer ends of theplates 26 and 27 may be pressed toward each other, as shown in Fig. 2,in which case these plates will engage the opposite edges of ,the tapeand will hold the same against displacement relatively to the arrow orindicator 30 so that the answer may be read at the convenience of theperson using the calculating device.

In order to make this possible, the cylinder 25 is notched or recessedat opposite sides, as indi- '159 resaca@ cated at 31 in Figs. 2 and 7,or if the cvlindei` is rotatable about its axis, this can be madepossible by having the recesses extend completely around the ends of thecylinder so that the tape extends slightly beyond the ends of theperipheral portion of the cylinder.

In order to avoid error in the answer resulting from the improperholding of the finder relatively to the tape, the plates 26 and 27 haveextensions 32 which are provided near their edge portions withgraduations 33 spaced equally from the center lines of the plates. Thefinder will be in correct position with reference to the tape when thecentral plane of the nder lies midway bed tween the two parts of thetape extending to the nder, and consequently the nder will be in thiscorrect posiion when the two parts of the tape adjacent to thegraduations 33 are spaced at equal distances from the central line ofthese graduations, and this spacing of the tape relatively to the findercan easily be determined by means o the graduations 33.

When it is necessary to use the device for multiplying two numbers, thegraduations of which are so close together that the slide 20 can- `notbe used, the two plates 26 and 27 may be profrom the central plate ofthe finder and, consequenly, when it is desired to multiply two numberswhich are close together on the tape, in-

stead of bringing these numbers into registration with each other, thetwo numbers are placed at equal distances from the indicator 30, suchdistances being readily determinable by the aid of the graduations 35.In this way, the middle point between the two graduations can be quicklyfound. The necessity of working with two graduations spaced closelytogether can, of course, be avoided by repeating at least portions ofthe sets of graduations at opposite ends of the main se't of graduationson the tape. By extending the length of the extensions 32 of the sideplates 26 and 27, this method of nding the half-way point could becarried on to a greater extent than shown in the drawing.

Other means than the two shown for finding the midway point between twopoints on the tape can f be employed if desired.

Preferably, the case 12 is made tov receive at least a part of thefinder to hold the same when not in use, and for this purpose, in theparticular construction illustrated, the winding drum or spool 11 isspaced from the opposite side walls of the case 12 to a sufficientextent to permit parts of the plates 26 and 27 to enter into the caseand straddle the drum or spool, as shown in Fig. 7. A retaining spring37 maybe arranged on a side of the casein such a way as to releasablyengage with an end of the central pin 24 extending through the cylinder25, and thus hold the finder in place on the case. The end oi the tapemay be provided with an enlarged outer end 38 which will not passthrough the slot 2l in the slide 20 so that when the device is not inuse the parts may be mounted thereon, as shown in Fig. 5. The tension ofthe spring 10 in this case also tends to hold the nder on the case. Anyother means may be employed for detachably holding the parts of thedevice together when not 1n use.

The device described has the advantage that the tape can be made of thinmaterial, such as metal, so that a considerable length can be wound upona relatively small spool or pulley. This permits the graduations to bemade on a large enough scale to provide for accuracy equivalent to thatof a slide rule of substantially the same length. When the device is notin use, the tape occupies very little space so that the entirecalculating device occupies only a very small fraction of the spacewhich would be occupied by a slide rule of corresponding accuracy.

I claim as my invention:

l. A calculating device having two sets of parallel, coextensivegraduations, one set of graduations being twice the number of andproportionally spaced with respect to the graduations of the other set,the graduations being given the same value designations and arranged inthe same order in both sets of graduations, and rnechanical meansassociated with said sets and operable for directly indicating themidpoint between any two points on one set.

2. A calculating device having a plurality of sets of proximateparallel, coextensive unit graduations, the number of graduations ofeach set being a multiple of the number of graduations in another ofsaid sets, the unit graduations of all sets being proportionately spacedwith respect to those of the other sets, given the same valuedesignation, and arranged in the same order, and mechanical meansoperable endwise with respect to said sets and cooperating therewith fordirectly indicating a selected, multiple division point between any twopoints on one set.

3. A calculating device having a flexible tape provided on a lengthwiseportion thereof with a set of graduations and having on a coextensiveportion thereof a second set of graduations formed on a smaller scalesuch that a definite number of said second sets of graduations occupy alength of said tape coextensive with the length of said rst set, andmeans associated with said tape to find on said second set ofgraduations a point half way between two points on said first set ofgraduations.

Il. A calculating device, including a graduated strip provided on alengthwise portion thereof with a set of graduations and having on acoextensive parallel lengthwise portion thereof a second set ofgraduations formed on half of the scale oi said first set ofgraduations, and means associated with said strip for finding on saidsecond set of graduations a point half-way between two points on saidiirst set of graduations.

5. A calculating device, including a graduated flexible tape provided ona lengthwise portion thereof with a set of graduations and having on aco-extensive parallel lengthwise portion thereof flexible tape providedon a lengthwise portion` thereof with a set of graduations and having ona coextensive lengthwise portion thereof a second set of graduationsformed on half of the scale of the rst set of graduations, said tapebeing adapted to be bent to place two graduations of said first set intoregistration, a device having a curved surface over which a. portion ofthe tape intermediate of said graduations extends, and means on saiddevice to indicate a point on the tape which is midway between saidregistering graduations.

'7. A calculating device including a flexible tape and havinggraduations thereon and adapted to be bent to place two graduations ondifferent parts of the tape into registration, and a device cooperatingwith said tape for finding a point thereon midway between saidregistering graduations, said device including an indicator, which, whenthe portion of the tape between said registering graduations is pulledtaut, will be at said midway point.

8. A calculating device including a flexible tape and having graduationsthereon and adapted to be bent to place two graduations on diilerentparts of the tape into registration, and a device cooperating with saidtape for finding a point thereon midway between said registeringgraduations,

' said device including a curved part against which said tape bears whenthe portion of the tapebetween said registering graduations is pulledtaut, and side members arranged to engage the opposite side edges of thetape to hold the same in correct relation to said curved part, and agraduation on said device indicating the midway point of said portion oftape between said registering graduations.

9. A calculating device including a flexible tape having graduationslengthwise thereof Y and adapted to be bent to place two registrationson different parts of said tape into registration, and a device fornding the midway point between said registering graduations, said deviceincluding a curved part against which a portion of the tape bears whenthe part ofthe tape between said registering graduations is pulled taut,side members connected with said curved part and arranged to engage theedges of said tape and having a part extending towards said registeringgraduations, said part having graduations for indicating when said sidemembers are in correct relation to said registering graduations, andmeans on one of said side members for indicating the point on said tapelocated midway between said registering graduations. g

10. A calculating device including a strip having graduations arrangedlengthwise thereon, and a device arranged to cooperate with said stripfor finding a point thereon midway between two graduations of saidstrip, including an indicator arranged to point to said midway point onthe strip, and graduations on said device, equally spaced from saidindicator, with reference to which graduations on said strip may bespaced at equal distances from said indicator.

11. A calculating device including a flexible strip provided withgraduations arranged lengthwise thereon, and a device for use in findinga point midway between two graduations on said strip, said deviceincluding a curved surface over which a part of said strip may be bent,an indicator on said device for indicating a point halfway between twograduations on said strip, and graduations on said device extendingtoward opposite sides of said indicator for use in connection with thespacing of two graduations on said strip at equal distances from saidindicator.

12. A calculating device including'a graduated strip of flexiblematerial, said strip being adapted to be bent to place two graduationson different parts of the strip into registration,means for determiningthe point on said strip midway between said registering graduations, anda member slidably arranged on said strip and movable into registrationwith one of said registering graduations and having a part adapted toreceive the portion of the strip carrying the other registeringgraduation to facilitate the placing of said graduations intoregistration.

13. A calculating device including a graduated exible tape, a spool onwhich the same may be wound, a case in which said spool is contained andopen at an edge portion to permit the tape to be drawn out of said case,a devi-ce adjustable lengthwise of said tape for use in determining apoint midway between two graduations on said tape, and means on saidcase for receiving a portion of said device to hold the same inconnected relation to said case.

14. A calculating device including a graduated iexible tape, a spool onwhich the same may be wound, a spring for turning said spool in adirection to wind the tape thereon, a device movable lengthwise of saidtape for determining a point midway between two graduations on said tapeand having parts adapted to enter into said case, said spring serving toyieldingly hold said device in operative relation to said case when saiddevice is not in use.

JAMES F. SUMMERS.

